Numerical simulation of thermal problems coupled with magnetohydrodynamic effects in aluminium cell |
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Authors: | Y. Safa M. FlueckJ. Rappaz |
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Affiliation: | Institute of Analysis and Scientific Computing, École Polytechnique Fédérale de Lausanne, Station 8, 1015 Lausanne, Switzerland |
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Abstract: | A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered as a two-phases Stefan problem which consists of a non-linear convection–diffusion heat equation with Joule effect as a source. The magnetohydrodynamic fields are governed by Navier–Stokes and by static Maxwell equations. A pseudo-evolutionary scheme (Chernoff) is used to obtain the stationary solution giving the temperature and the frozen layer profile for the simulation of the ledges in the cell. A numerical approximation using a finite element method is formulated to obtain the fluid velocity, electrical potential, magnetic induction and temperature. An iterative algorithm and 3-D numerical results are presented. |
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Keywords: | Aluminium electrolysis Chernoff scheme Heat equation Magnetohydrodynamics Ledge Solidification |
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